We propose a mapping between geometry and kinematics that implies the classical equivalence of any theory of massless bosons—including spin and exhibiting arbitrary derivative or potential interactions—to a nonlinear sigma model (NLSM) with a momentum-dependent metric in field space. From this kinematic metric we construct a corresponding kinematic connection, covariant derivative, and curvature, all of which transform appropriately under general field redefinitions, even including derivatives. We show explicitly how all tree-level on-shell scattering amplitudes of massless bosons are equal to those of the NLSM via the replacement of geometry with kinematics. Lastly, we describe how the recently introduced geometric soft theorem of the NLSM, which universally encodes all leading and subleading soft scalar theorems, also captures the soft photon theorems.

中文翻译：

---

几何运动学对偶

我们提出了几何和运动学之间的映射，这意味着任何无质量玻色子理论（包括自旋和展示任意导数或潜在相互作用）与场空间中具有动量相关度量的非线性 sigma 模型 (NLSM) 的经典等价性。从这个运动学度量中，我们构造了一个相应的运动学连接、协变导数和曲率，所有这些都在一般场重新定义下适当地变换，甚至包括导数。我们通过用运动学替换几何，明确展示了无质量玻色子的所有树级壳上散射幅度如何等于 NLSM 的那些。最后，我们描述了最近引入的 NLSM 几何软定理如何普遍编码所有领先和次领先的软标量定理，